1. Field of the Invention
The present invention relates generally to satellites and more particularly to optimized positioning of a satellite's solar wings.
2. Description of the Related Art
Satellites are placed into orbit paths about celestial bodies (e.g., planets and suns) to facilitate a variety of missions (e.g., communications, surface mapping, atmospheric studies and celestial observations). FIG. 1 illustrates an exemplary body-stabilized satellite 20 which travels along an orbit path 22 that defines an orbit plane 24 about the Earth 25. Carried on or within the satellite's body 26 are various operational systems, e.g., a communications system which includes antennas 28, a propulsion system which includes thrusters 30 and an energy-generation system which includes a solar array comprising solar wings 32 and 34.
In a body-stabilized satellite, solar wings are generally placed on opposite sides of the orbit plane 24 and oriented so that solar radiation of the planet's sun (not shown) is incident upon the wings' solar cells. This radiation is parallel to a sun line 36 between the sun and the satellite 20. If the sun line 36 were always in the orbit plane 24, maximum energy generation would be obtained by simply positioning the solar wings 32 and 34 orthogonal to the orbit plane and rotating them at orbit rate in the direction that maintains area-normal vectors 27, 37 (vectors which are respectively normal to solar wings 32, 34) parallel to the sun line 36 as the satellite travels along its orbit path 22. Generally, however, the sun line 36 moves seasonally with respect to the orbit plane 24, and as a result, the power from orbit normal solar wings is near its maximum for only .about.20% of the year.
For example, FIG. 2 illustrates the satellite 20 in a geostationary orbit in which its orbit plane 24 is coplanar with the earth's equatorial plane 39 and its circular orbit period is equal to one earth day. Thus, the orbit normal 40 and the earth's equitorial pole 41 are colinear. From the perspective of the satellite's body-fixed reference frame (shown as axes 31, 33 and 35 in FIG. 1), the sun, over the course of one day, appears to travel about the earth 25 and the satellite's body 26, and the sun line (36 in FIG. 1) appears to trace out a conical surface (42S for summer solstice) which is symmetrically inclined from the equitorial plane 39 by a sun elevation angle .beta. that varies continuously in the range -23.45 to +23.45 degrees over the course of a year. Various conical surface cross-sections are shown in FIG. 2, 42S for a summer solstice day, 42E for a fall or spring equinox day, and 42W for a winter solstice day. The earth's sun 44 is also shown as it would appear to the satellite each season at summer solstice 44S, at fall and spring equinoxes 44E and at winter solstice 44W. It is apparent from FIG. 2 that if the solar wings 32 and 34 were controlled to be orthogonal to the orbit plane 24, they would be orthogonal to the sun line (36 in FIG. 1) only at fall and spring equinoxes.
In general, the energy generated by a solar array is approximately defined by EQU P=eP.sub.0 Acos.beta. (1)
in which e is solar array efficiency, P.sub.0 is solar illumination energy incident on the array and A is total solar array area. Equation 1 is written in a simplified form which combines each solar wing's area into the total array area A, and assumes that each solar wing's area normal vector 27 and 37 is coplanar with the sun line 36 and parallel with the orbit plane 24.
The solar array efficiency e falls off during a satellite's lifetime for various reasons (e.g., radiation-induced flaws in the crystal structure of the solar cells, radiation-induced deterioration of the transparency of solar cell protective shields and thermally-induced reductions in solar cell performance). The solar illumination P.sub.0 varies in a predictable periodic manner because the earth's seasonal distance to the sun is not constant but varies in accordance with the plot 48 in the graph 50 of FIG. 3. Note that the distance in graph 50 at summer solstice is .about.3% greater than the distance at winter solstice. The angle of the sun's elevation .beta. with respect to the satellite's orbit also varies in a predictable, periodic manner according to the plot 49 in graph 50 of FIG. 3.
FIG. 4 shows a graph 60 which has a plot 62 of power from a typical set of planar solar wings that are positioned to be orthogonal to a geostationary orbit plane. The plot 62 indicates power reduction over the satellite's lifetime that results from the reduced solar array efficiency. In addition, the plot 62 varies seasonally because of the variation in the sun's elevation angle .beta. and the variation in solar distance (shown in FIG. 3). In each seasonal variation, the power at a summer solstice point 64 is .about.15% less than it is at a respective spring equinox point 65. Each seasonal variation also includes the power at a fall equinox point 66 and a winter solstice point 67. Because of the seasonal and long-term effects, the power at a beginning-of-life (BOL) spring equinox differs from an end-of-life (EOL) summer solstice by a lifetime power differential 68. Typically, the BOL spring equinox power is .about.33% greater than the EOL summer solstice power for a satellite with a 15 year lifetime.
Because prudent satellite design requires the satellite's systems to operate at the EOL summer solstice power, the additional power at other periods of the satellite's lifetime is typically "thrown away" (e.g., dissipated in voltage limiting circuits and radiated out to space) with consequent increase in a satellite's volume, weight and cost (or, alternatively, a decrease in payload) because the satellite's thermal control system must include apparatus (e.g., greater radiating surfaces and larger heaters) to accommodate the wide range of thermal capacity over life.
Solar wing structures and methods have been proposed to reduce a satellite's lifetime power differential (as exemplified by the power differential 68 of FIG. 4). For example, copending U.S. patent application Ser. No. 08/690,702 (entitled "Satellite Solar Array and Method of Biasing to Reduce Seasonal Output Power Fluctuations", filed Jul. 31, 1996, and assigned to Hughes Electronics, the assignee of the present invention) is directed to an increase in the worst case minimum output power of a satellite's solar array. Similar to conventional satellites, the solar arrays of this reference rotate about a rotation axis that is controlled to be orthogonal to the satellite's orbit plane.
In contrast to conventional satellites, however, the solar wings are tilt-biased at a fixed attitude with respect to the rotation axis. In an exemplary geostationary satellite, the wings are tilt-biased .about.4 degrees closer to a sun-normal orientation for the sun's position at summer solstice. Accordingly, the solar array's output power at summer solstice (64 in FIG. 4) would be increased by .about.3%. Because the output power at winter solstice (power point 67 in FIG. 3) would be reduced by a similar percentage, the output power at the two solstices would be approximately equalized. In an exemplary satellite structure, the fixed bias could be realized with a wedge that is positioned between each solar wing and its rotational drive mechanism.
U.S. patent application Ser. No. 08/690,702 further teaches that the minimum seasonal power of a solar array can be increased by providing a second rotational axis which would allow the solar array to track the seasonal elevation movement of the sun. The concept of an additional rotational axis is also taught in German Patent WO92/19498. This Patent is directed to satellite attitude control by means of solar pressure torques on a pair of solar wings which are oriented in opposite directions from the satellite's body. In particular, solar pressure torques are generated about two axes of a body coordinate system by adjusting the solar wings in opposite angular directions about a first rotational axis and solar pressure torques are generated about a third axis of the body coordinate system by adjusting the solar wings in opposite angular directions about the second rotational axis.
Satellite attitude control is also the subject of U.S. Pat. No. 5,310,144. A preferred satellite attitude (e.g., one which keeps the communications antennas of the satellite 20 of FIG. 1 directed toward the earth 25) is typically maintained by absorbing the momentum generated by environmental torques with the satellite's momentum-management system (e.g., by changing the angular velocity of flywheels). When this system's momentum capacity is reached, momentum must be "dumped" by generating opposing momentum components (e.g., by firing thrusters of the satellite's reaction-control system).
U.S. Pat. No. 5,310,144 recognizes that the size of the momentum-management system and the energy use of the reaction-control system could both be reduced by tilting the satellite's solar wings toward or away from the sun (about an axis normal to the sun line) to reduce environmental overturning torques. In a method of this Patent, a disturbance torque (principally generated by solar pressure and gravity gradients) is measured, solar wing tilt angles are determined which will minimize the disturbance torque and the solar wings are tilted by the determined angle. While this wing tilting can reduce overturning torques, the Patent acknowledges that it will also cause a modest solar power degradation.
Although these references address angular positioning of solar wings to increase worst case power generation or to enhance attitude control (via environmental torques), they address these different concepts in isolation, and thus, fail to recognize or take advantage of the interactions between them. Accordingly, they fail to provide methods for favorably reducing seasonal variations of generated power while simultaneously managing environmental torques and other system influences associated with off-pointing the solar wings.